POLE ASSIGNMENT IN VIBRATORY SYSTEMS BY MULTI-INPUT CONTROL

The problem of reassigning some poles of a vibratory system, while keeping the other poles unchanged, is considered. The problem may be solved uniquely by single-input state feedback control. A family of solutions to the partial pole assignment problem may be obtained by applying multi-input control forces. An algorithm for determining a multi-input control which is small in some sense is presented. The non-iterative algorithm proposed, defines a closed-form solution to the partial pole assignment problem in its natural second order form, and no first order realization is used. The reduction in the control effort achieved by the proposed method is demonstrated by numerical examples.